The weights of the fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the likelihood that the mean weight will be between 12.6 and 18.6 Lb?

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Quizplus · Accepted Answer

The sampling distribution of the sample mean for a normally distributed population is also normal with a mean equal to the population mean (μ = 15 lb) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/√n = 6/√4 = 3). To find the probability that the sample mean is between 12.6 and 18.6, we use the standard normal distribution (Z). Z = (X - μ) / (σ/√n). For X = 12.6, Z = (12.6 - 15) / 3 = -0.8. For X = 18.6, Z = (18.6 - 15) / 3 = 1.2. Using standard normal distribution tables or a calculator, the probability of Z being between -0.8 and 1.2 is approximately 0.6730.

The Weights of the Fish in a Certain Lake Are